A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data

ABSTRACT Interval-censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis. However, most of the existing methods are for univariate data and there exists only limited research on bivariate data, especially on regression analysis of bivariate interval-censored data. We present a class of semiparametric transformation models for the problem and for inference, a sieve maximum likelihood approach is developed. The model provides a great flexibility, in particular including the commonly used proportional hazards model as a special case, and in the approach, Bernstein polynomials are employed. The strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore, the estimators are shown to be asymptotically efficient. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. Supplementary materials for this article are available online.

[1]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[2]  Xiaoyan Lin,et al.  A semiparametric probit model for case 2 interval‐censored failure time data , 2010, Statistics in medicine.

[3]  L. J. Wei,et al.  Regression analysis of multivariate incomplete failure time data by modeling marginal distributions , 1989 .

[4]  Xiaotong Shen,et al.  On methods of sieves and penalization , 1997 .

[5]  Joseph G Ibrahim,et al.  Gamma frailty transformation models for multivariate survival times. , 2009, Biometrika.

[6]  Z. Ying,et al.  Analysis of transformation models with censored data , 1995 .

[7]  Jian Huang,et al.  Efficient estimation for the proportional hazards model with interval censoring , 1996 .

[8]  Xingwei Tong,et al.  A linear transformation model for multivariate interval‐censored failure time data , 2013 .

[9]  Peter McCullagh.  Proportional‐Odds Model , 2005 .

[10]  Richard J Cook,et al.  A Multistate Model for Bivariate Interval‐Censored Failure Time Data , 2008, Biometrics.

[11]  D. Lin,et al.  Regression analysis of multivariate grouped survival data. , 1994, Biometrics.

[12]  Xingwei Tong,et al.  A frailty model approach for regression analysis of multivariate current status data , 2009, Statistics in medicine.

[13]  Xingwei Tong,et al.  The proportional odds model for multivariate interval‐censored failure time data , 2007, Statistics in medicine.

[14]  Jian Huang,et al.  Sieve Estimation for the Proportional-Odds Failure-Time Regression Model with Interval Censoring , 1997 .

[15]  Ding-Geng Chen,et al.  Interval-Censored Time-to-Event Data: Methods and Applications (Chapman & Hall/CRC Biostatistics Series) , 2012 .

[16]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[17]  D. Finkelstein,et al.  A proportional hazards model for interval-censored failure time data. , 1986, Biometrics.

[18]  Zhiliang Ying,et al.  On the linear transformation model for censored data , 1998 .

[19]  Zhigang Zhang,et al.  Regression analysis of interval‐censored failure time data with linear transformation models , 2005 .

[20]  D. Park.  The Statistical Analysis of Interval-Censored Failure Time Data , 2007 .

[21]  W. Wong,et al.  Convergence Rate of Sieve Estimates , 1994 .

[22]  Xingwei Tong,et al.  Regression Analysis of Multivariate Interval‐Censored Failure Time Data with Application to Tumorigenicity Experiments , 2008, Biometrical journal. Biometrische Zeitschrift.

[23]  Naichen Wang,et al.  Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm , 2015, Comput. Stat. Data Anal..

[24]  Yi-Hau Chen,et al.  Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model , 2011, Comput. Stat. Data Anal..

[25]  D. Finkelstein,et al.  A Proportional Hazards Model for Multivariate Interval‐Censored Failure Time Data , 2000, Biometrics.

[26]  Juan Manuel Peña,et al.  Shape preserving representations and optimality of the Bernstein basis , 1993, Adv. Comput. Math..

[27]  Xingwei Tong,et al.  Efficient estimation for the proportional hazards model with bivariate current status data , 2008, Lifetime data analysis.

[28]  Donglin Zeng,et al.  Semiparametric additive risks model for interval-censored data , 2006 .

[29]  James R. Kenyon,et al.  Analysis of Multivariate Survival Data , 2002, Technometrics.

[30]  Sujit K. Ghosh,et al.  Nonparametric regression models for right-censored data using Bernstein polynomials , 2012, Comput. Stat. Data Anal..

[31]  C. Wen,et al.  A FRAILTY MODEL APPROACH FOR REGRESSION ANALYSIS OF BIVARIATE INTERVAL-CENSORED SURVIVAL DATA , 2013 .

[32]  D Sinha,et al.  Bayesian Analysis and Model Selection for Interval‐Censored Survival Data , 1999, Biometrics.

[33]  T. Goodman.  Shape preserving representations , 1989 .

[34]  D. Lin,et al.  Cox regression analysis of multivariate failure time data: the marginal approach. , 1994, Statistics in medicine.